Question

1. in quadrilateral defg below, dg is parallel to ef.

what is the measure of ∠f?
a. 85°
b. 95°
c. 75°
d. 105°

1. trapezoid rstu is shown below with st parallel to ru.

what is m∠s?
a. 56°
b. 45°
c. 124°

Explanation:

Step1: Use the property of consecutive interior angles

Since \(DG\parallel EF\), \(\angle F+\angle G = 180^{\circ}\) (consecutive - interior angles). Given \(\angle F=(x + 10)^{\circ}\) and \(\angle G=x^{\circ}\), then \((x + 10)+x=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(2x+10 = 180\). Subtract 10 from both sides: \(2x=180 - 10=170\). Divide both sides by 2: \(x = 85\).

Step3: Find the measure of \(\angle F\)

Substitute \(x = 85\) into \(\angle F=(x + 10)^{\circ}\). So \(\angle F=(85 + 10)^{\circ}=95^{\circ}\).

Step1: Use the property of consecutive interior angles in a trapezoid

Since \(ST\parallel RU\), \(\angle R+\angle S = 180^{\circ}\) (consecutive - interior angles). Given \(\angle R = 56^{\circ}\).

Step2: Calculate \(\angle S\)

We know that \(\angle S=180^{\circ}-\angle R\). Substitute \(\angle R = 56^{\circ}\) into the formula: \(\angle S=180 - 56=124^{\circ}\).

Answer:

B. \(95^{\circ}\)